Week 2 ANOVA from Slides Flashcards
To cover: One-way ANOVA Factorial between-groups ANOVA purpose & assumptions Main effects and interactions Signal to noise ratio in F tests How variability is apportioned in a 2-way ANOVA Calculations of error in a 2-way ANOVA Other analyses such as missing cell designs Family wise error adjustment & simple comparisons Graphing an interaction in a research report
When can I use an ANOVA?
ANOVA may be used when I am comparing more than two levels of an IV on a single continuous DV.
How might I define ANOVA?
- ANOVA provides a comparison of the variation between the average results per condition and the average variation within the different conditions.
- When more than one group is being analysed, each IV is known as a main effect.
- The groups or cells correspond to the various combinations of those IVs, and all the cells are independent
- The individual cells created from the cross product of the main effects, are known as “interactions” in factorial ANOVA.
What are the assumptions of ANOVA?
- The DV should be continuous in nature. (Scale in SPSS)
- Random assignment of individuals to groups
- The scores should be independent; appearing in only one cell
- The scores on the DV should be normally distributed
- Homogeneity of variance needs to be assessed & criteria met
- factorial ANOVA is robust against violations of the assumptions of normality & homogeneity of variance when cell sizes are large & equal
What does Kate emphasis with regard to the assumptions of ANOVA?
- The assumptions of ANOVA are very specific:
- Cell size should be between 20-30 for each cell.
- Use Levene’s to check homogeneity of variance, that is the variances in each cell populations are equal
- All ANOVA designs are less complicated if they are balanced, equal participants in each cell.
- Unbalanced designs, with unequal numbers in each cell are possible but more problematic and homogeneity of variance becomes even more critical
- There are no non-parametric tests for the more complex factorial ANOVAs.
Kate gives us a review of one-way ANOVA. What does she say about the “Signal-to-Noise” Ratios in F tests?
- When you have more than 2 groups you cannot use a t-test, instead you need to use ANOVA, the F test when using a single dependent variable.
- ANOVA may compare:
- between groups & within group variability
- the relationship between F and t
- Squaring t always produces F
- However, taking square root of F does not always equal t
What should I do if my Levene’s test for Homogeneity of Variance is violated?
- I can run Brown-Forsythe, which assumes that group variances are statistically equal. If this assumption is not met, the F test is invalid.
- Brown–Forsythe test transforms the response variable on the absolute deviations from the median not the mean.
- Also Games-Howell should be used as a Post Hoc analysis.
How do I interpret the ANOVA table?
*There is a between groups condition = the “signal”
*the Within groups condition = the “noise” / Error variance
*to get the significance levels:
divide ‘mean square between’ by ‘mean square within’ = F statistic.
*Look up the F statistic in the table of critical values, according to df groups by within group df.
*I aim for the significance level to be less than .05
How is Variability Apportioned in a One-Way ANOVA?
Variance is broken into:
*Systematic variation between groups or condition
(aka signal variation)
*Error variation within groups or conditions
(aka noise variation)
*The F-statistic is a simple ratio of:
The ‘variance between groups’ divided by
The ‘variance within groups’ (or error variance)
*MSb/MSw = F ratio
What is the actual process if I wanted to computer a one-way ANOVA by hand (like we used to 4 years ago)?
During a one-way ANOVA, variability is apportioned by evaluating the signal, that is the systematic variation between groups or conditions as well as the noise variation, that is the Error variance or the within groups or conditions variance.
The variance equation is achieved by adding all the raw scores together & minus-ing the mean squared, then dividing it by the degrees of freedom.
What are the crucial degrees of freedom for a One-Way ANOVA?
Between groups df = k-1 (where k = # of groups) and,
Within groups df = N – k (N is total no. of participants)
Total df= N-1 for (where N = total # of participants)
So, what can you tell me about the Variance Between and the Variance within group?
- If the variation between groups is the same as the variation within groups, then the F ratio = 1, Ho is true.
- If the value is larger than 1, then it is necessary to check the F value obtained & compare it to a critical table.
- I need to check dfb and dfw to assess whether the critical value is significant and level of significance for reporting.
Okay, so I know the ANOVA has some significance, but where? What do I do next to identify which group(s) are significant?
- I use the Tukey’s Honestly Significant Difference (HSD) Multiple Comparisons post hoc test
- This table tells me exactly where the significance is
What does the part of the Tukey’s table “subsets for Alpha = 0.05 indicate?
- This table displays means for groups in homogeneous subsets
- I want my group means to be in subset 1 or subset 2
- There is a problem if they are in both as this means they are not distinct (homogeneity)
What can you tell me about effect size with One-Way ANOVA?
*Differences exist in partial effect size (np) and effect size.
*The effect size np given in SPSS in GLM models is evaluated by dividing the “Sum of Squares between”, by the “Sum of Square corrected total” (which is the grand mean total sum of squares).
However, in other ANOVA designs, it is not appropriate to use partial eta square.
*calculation of Omega is sometimes a preferred measure of effect size. Which needs to be manually calculated.
When marginal cells are equal in size, marginal means have the same values as the observed means; however, in other forms of ANOVA I may come across marginal means which differ from the descriptives. Why is this?
When cell sizes are unequal, the marginal means are unweighted means, and they differ from the Descriptive Statistics tables.
*Unweighted means are simply the average of the contributing cell means, so each cell contributes equally, regardless of its size
